Hong Ou Mandel experiment with atoms

Chris WestbrookLaboratoire Charles Fabry, Palaiseau

FRISNO 13, Aussois 18 march 2015

BEC on an MCP

2 particles at a beam splitter

1 particle at each input → 4 possibilities:

both transmitted

both reflected

d

ca

b

both in c both in d

2 particles at a beam splitter

1 particle at each input → 4 possibilities:

both transmitted

both reflected

d

ca

b

both in c both in d

Hong Ou Mandel effect: only 2 possibilities

Hong, Ou and Mandel PRL 59, 2044 (1987)

d

c

〈nc〉 = 〈nd〉 ≠ 0

〈ncnd〉 ≈ 0

“HOM dip” as a function of the overlap between the two arms.

d

ca

b

2 classical wave packets

Ic

Id

𝜙

d

ca

b

2 classical wave packets

Ic

Id

0.0 0.5 1.0 1.5 2.0

0.51.01.52.0

0 π 𝜙

IcId

𝜙

d

ca

b

2 classical wave packets

Ic

Id

0.0 0.5 1.0 1.5 2.0

0.51.01.52.0

0 π 𝜙

IcId

𝜙

correlation function:

g(2)cd = = 1/2 overlapped

g(2)cd =1 not overlapped (detector slower than pulse)

〈Ic Id〉𝜙

〈Ic〉𝜙〈Id〉𝜙 pulse delay

1

0.5

2 quantum fields at a beam splitter

1 particle at each input → 4 QM amplitudes:

both transmitted

both reflected

d

ca

b

2 quantum fields at a beam splitter

1 particle at each input → 4 QM amplitudes:

both transmitted

both reflected

d

ca

b

G(2)cd = 〈ncnd〉 = 0two particle interference has no classical analog

§ 1, 1\a,b = a† b†• 0, 0] = 12Ic† + d†M I-c† + d†M• 0, 0]

= 12I-c†2 + d†2 + c† d† - d† c†M• 0, 0]

= 12H -§ 2, 0\c,d +§ 0, 2\c,d )

Why do it?

Santori et al. “Indistinguishable photons from a single-photon device” Nature, 2002 (one quantum dot)

Beugnon et al. “Quantum interference between two single photons emitted by independently trapped atoms” Nature, 2005

It’s cool...Tests single photon sourcesMetrology with twin Fock states

How to do it with atoms

Essential features

photon coincidence counting → He*, MCP

source of photon pairs → 4 wave mixing

mirrors, beam splitter → Bragg diffraction

spatial, spectral filters → MCP

Get a good team

Pierre Dussarat Almazbek ImanalievMarc Cheneau

Denis BoironC I W Raphael LopesAlain Aspect

Metastable Helium, He*

Lifetimes:23S1: 8000 s23PJ: 100 ns

4He (no nuclear spin)

deexcitation enables electronic detection: He*→He+ + e-

microchannel plate and delay line anode spatial resolution ~250 µmq.e. > 25%

23S1

21S0

11S0

23P0,1,2

1083 nm

E (eV)

0

19.8

20.6

24.6

“Time of flight” observation

5×104 detectors in // record x,y,t for every detected atomget velocity distribution and correlation functions

trap

detector

46 cm

there is also a laser trap

“Time of flight” observation

5×104 detectors in // record x,y,t for every detected atomget velocity distribution and correlation functions

trap

detector

46 cm

there is also a laser trap

Pair production: 4 wave mixing in a latticedynamical instability: 2 k0 → k1 + k2

Hillingsoe and Molmer, PRA 2005Campbell et al. PRL 2006Bonneau et al. PRA 2013

lowest energy band

Pair production: 4 wave mixing in a latticedynamical instability: 2 k0 → k1 + k2

Hillingsoe and Molmer, PRA 2005Campbell et al. PRL 2006Bonneau et al. PRA 2013

lowest energy band

Pair production: 4 wave mixing in a latticedynamical instability: 2 k0 → k1 + k2

Hillingsoe and Molmer, PRA 2005Campbell et al. PRL 2006Bonneau et al. PRA 2013

lowest energy band

Bragg diffraction: mirror and beam splitter

kBragg-1𝜃

Angle 𝜃 adjusted so that kBragg = k2 - k1

100 µs pulse : mirror 50 µs pulse : 50-50 beam splitter

k1 k2

Experimental sequence

zx

y

45 c

m

a

timeposi

tion

zt1 t2 t3

b

a

b

a

b

c

d

a

b

c

d

c

t1 pair creation

t2 mirror exchanges ka and kb t2-t1 = 500 µs

t3 beam splitter mixes 2 modes

atoms fall to detector

Detected

atomnum

ber

Detected atom number

a

0.00

0.04

0.08

0.12b

0.00

0.04

0.08

0.12c

6.0 7.0 8.0

-2.0 0.0 2.0

0.00 0.02 0.04 0.06

-2.0 0.0 2.0vx (cm/s)

v z (cm

/s)

7.0

9.0

11.0

13.0

vx (cm/s)

vz (cm/s)

Filtering

small slice of the velocity distribution isolates one mode

0.8 atoms/mode0.2 detected

vb

va

HOM correlation

W (P s)

0.00

0.02

0.04

0.06

0.08

150

G(2) cd

900750600450300

G(2)cd = 〈ncnd〉0.06 coincidences per shot

50% contrast

delay: 𝜏 = t3-t2

n.b. t2-t1 = 500 µs~10 hrs of data for each point

Lopes et al. arXiv:1501.03065

observed contrast is mostly due to multiple atoms

Other, non-optical experiments

AtomsKaufmann et al., Science 345, 306 (2014).

ElectronsBocquillon et al., Science 339, 1054 (2013).Dubois et al., Nature 502, 659 (2013).

PlasmonsFakonas et al., Nature Photonics 8, 317 (2014).Di Martino et al., Phys. Rev. Appl. 1, 034004 (2014)

MicrowavesLang et al., Nature Phys, 9, 345 (2013).

2 particle interference in a double well

Kaufmann et al., Science 345, 306 (2014)

Future

Bell’s inequalities without spin degrees of freedom |k1,q1〉 + |k2,q2〉 Lewis-Swann and Kheruntsyan 1411.0191Need to increase the repetition rate with low pair production (D. Clément: He* BEC in 7 s)

with photons:Rarity and Tapster PRL 1990

Multiparticle interference with spins

2 mode squeezed state in the spin sector

B. Lücke, et al « Twin Matter Waves for Interferometry Beyond the Classical Limit », Science, 334, p. 773-776 (2011).

Photonic version, Spasibko et al. NJ Phys 2014

Do it in momentum space?

Merci

Merci

Two obvious causes for G(2) ≠ 0:

1. Lack of indistinguishibility i.e. imperfect spatial overlap2. Occasional presence of more than 1 particle

n.b. G(2)aa = 〈a†a†aa〉 = 0 for the |1,1〉 state

We find Vmax = 0.6 ± 0.1.

Data consistent with “perfect indistinguishibility” but extra particles in the state.

Interference contrast

HOM “peak”?

〈ncnd〉

〈nc2〉

0.0

0.5

1.0

1.5

2.0

2.5

200 400 600 800

g(2

)cd

⌧(µs)

Mean count rates

W (Ps)150 900750600450300

0.08

0.06

0.04

0.02

0.00

0.16

0.20

0.24

0.16

0.20

0.24

��n c!

��n d!

c

b

a

� n c!

. �

n d! G(2) cd

〈nc〉, 〈nd〉

... are roughly constant

Variation of contrast with filter widthV

a b

'�v z (cm/s) '�v ŏ� (cm/s)0.2 0.4 0.6 0.8 1.0 0.4 0.5 0.6 0.7 0.8

0.0

0.4

0.8

Variance in the number difference

V =h(N1 �N2)2i � hN1 �N2i2

hN1 +N2i

N1, N2 ~ 100

Vmin ~ 0.75

4 wave mixing in a (moving) optical lattice

Energy and quasi-momentum conservation2k0 = k1+k2

2E0 = E1+E2

Hillingsoe and Molmer, PRA 2005Campbell et al. PRL 2006Bonneau et al. PRA 2013

Interactions produce a dynamical instability for large k0

A few characteristics

Final momenta can be chosen with k0

Turning lattice off stops interaction → atom number can be controlled

Including mean field

Bonneau et al. PRA 2013

Populations

beam bP0 = 0.9P1 = 0.090P2 = 0.005

beam aP0 = 0.82P1 = 0.16P2 = 0.021

measured

we infer 〈n〉 ≈ 0.5 - 0.8 depending on assumptions

A two mode squeezed state

Two mode squeezed state:

y\ = 1cosh r

S Htanh rLn n, n^Xn\ = sinh2 r

In our experiment Xn\ ª 0.7 Æ r ª 0.76. Probabilities for 0, 1 or 2 particles:

P0 ª 0.6P1 ª 0.24P2 ª 0.10

Correlated atom pairs

Correlation function for back to back pairsg(2)(p, –p+Δp)

0.05 krec

Jaskula et al. PRL 2010

Microchannel Plate

Single atom detectionq.e. ~ 25%

Detector photos

Delay lines MCP + Delay lines

8 cm

Four wave mixing of free atoms

a.k.a. “a collision”

H = � a1a2a†3a

†4 + h.c.

energy and momentum conservation:

k1 + k2 = k3 + k4

E1 + E2 = E3 + E4

restricts atoms to a spherical shell Perrin et al. PRL 2007

Detection MCP and delay line

hole separation: 24 µmspatial resolution ~250 µm5×104 detectors in // q. e. for He* ~ 25%

must be careful about saturation

time differences give the position on MCPrecord x, y, t for each atomreconstruct momentum distribution

! 4 wave mixing, seen in 3D

! 4 wave mixing, seen in 3D

Other methodswhy look for alternatives?small occupation per mode (0.1 - 0.01)not easily controlled

relaxation of transverse excitations in BEC Bücker et al. Nat Phys (2011)

modulation of speed of soundparametric downconversion of phonons (DCE)Jaskula et al. PRL (2012)

Wave particle duality

If we look for an anti-correlation, we find one〈ncnd〉 = 0 :Particle interpretation

single photon at a beam splitter (Grangier et al., EPL 1986)

If we look for interference, we find it:Wave interpretation

HOM is more subtle because neither interpretation works.

Interference fringes from single photons

(Grangier et al., EPL 1986)

Photon pairs

ω1, k1

ω2, k2

parametric downconversion:

H ~ b a1†a2† + h.c.

4 wave mixing:

H ~ b1 b2 a1†a2† + h.c.

A. Migdall, NIST

These processes have led to Bell’s inequality violations, squeezing, improvements in interferometry ...

Hong Ou Mandel effect

Start with 1 photon in each input → 4 QM amplitudes:

|2,0〉 + |0,2〉 1st two amplitudes cancel, leaving:

average number in one output port 〈N〉 = 1variance v = 〈N2〉 -〈N〉2 = 1 v = 1/2 without interference

both transmitted

both reflected

normalized variance V = v/v = 2

Laser trap and detector

position at detector gives initial velocity